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Ok here's a puzzle:

If a, b, c & d are all integers and the following two criteria apply:

1/a + 1/b + 1/c + 1/d = 1

a <= b <= c <= d

how many solutions are there?

John (from A)

This is Quite Interesting, is there an elephant involved here, he said, or maybe a squirrel?

\"EEOOGH, EEOOGH\" Oh Sh#t, minus 20 points

Alan

Well the thread title is "Poser of the Day". Now if you are a Daily Sport or Daily Record reader you will have a new poser every day, but this is more of a puzzle than a poser and it can be solved by simple logic. A glass or two of good Cabernet may ease the way as well.

is it - 1?
a. b. c. d, are all 4?

24 ? (mix of +'s .... oh, sugar . I give up.

No, it's more than 1.

Anyway it's time for my cocoa now so I'll leave you all to think about it and give you the answer tomorrow.

There are an infinite number of solutions.

If we take b=2 & c=2 then, for example, one solution has a=-3 & d=3:

  1/(-3) + 1/2 + 1/2 + 1/3 = 1

Another solution would be with a=-4 & d=4:

  1/(-4) + 1/2 + 1/2 + 1/4 = 1

Any (of the infinite number of integer) values for a & d that cancel each other out would work.

JimC

Nope, not gettng it.
why assume "b=2 & c=2"?

Hi Trevor.

Sorry for the delayed reply - sleep got me.

Taking b=2 & c=2 just let me show easily why there might be an infinity of solutions.

There are other solutions in which b & c are not = 2 (such as the one you pointed out in which a=b=c=d=4) but the conclusion (that there are an infinity of solutions) still holds.

JimC

If the sun lightens your hair, why does it darken your skin?